What do you mean by "normal"? According to the game text, you're supposed to roll d4's, discarding the result "4".You're certainly changing some probabilities around if you're playing the "d6, discard 5 and 6" way. What dice do Intimacy, Desperation and Sincerity get in your version?This thread and this one dating from the playtesting may provide some information as to why the rules are the way they are today.

The 0-3 range for each die also makes the Intimacy d4 (1-4), Desperation d6 (1-6), and Sincerity d8 (1-8) worth that much more.

Playing with d6es and discarding 5's and 6's is a slightly different result curve, as the results on each die are {0,0,1,2,3,4} (mean 1.67) instead of {0,1,2,3} (mean 1.5). However, the range is quite different on the top end, since 4d{0,0,1,2,3,4} ranges from 0-16 but 4d{0,1,2,3} ranges from 0-12. What this accomplishes mechanically is to reduce the power of the Intimacy/Desperation/Sincerity mechanic by a couple points.

Will this ruin play? I don't think so. All the rolls in the game are opposed rolls anyway, so you're rolling weird new odds vs. weird new odds. If you're concerned about changing the I/D/S probabilities, shift each one of them up a die size (to d6/d8/d10).

Sometimes I have trouble finding enough d4's. Some people hate rolling d4's. So I can see the appeal of using d6 instead.